Answer:
The area of the figure is 3.6257188 cm²
The perimeter of the shape is 7.0685835 cm
Step-by-step explanation:
Let us find the area of the shape at first
∵ The shape formed from 3 semicircles and an equilateral triangle
∴ Its area = 3 (area of a semicircle) + area of an equilateral Δ
∵ Area of the semicircle = [tex]\frac{1}{2}[/tex] π r²
∵ The diameter of the semicircle = 1.5 cm
∵ The radius = [tex]\frac{1}{2}[/tex] the diameter
∴ r = [tex]\frac{1}{2}[/tex] × 1.5 = 0.75 cm
∴ The area of a semicircle = [tex]\frac{1}{2}[/tex] π (0.75)²
∴ The area of a semicircle = 0.28125π cm²
→ Find the area of the Δ
∵ Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
∵ The base of the triangle = 1.5 cm
∵ The height of the triangle = 1.3 cm
∴ Area of the triangle = [tex]\frac{1}{2}[/tex] × 1.5 × 1.3
∴ Area of the triangle = 0.975 cm²
→ Now find the area of the shape
∵ Its area = 3(0.28125π) + 0.975
∴ Its area = 3.6257188 cm²
∴ The area of the figure is 3.6257188 cm²
Now let us find the perimeter of the figure
∵ The perimeter of a figure is the length of the outline sides
∴ The perimeter of the figure = the length of the 3 half circumferences
∵ The length of half the circumference = [tex]\frac{1}{2}[/tex] (2 π r) = π r
∵ r = 0.75 cm
∴ The length of half the circumference = 0.75 π
→ Find the perimeter of the shape
∵ The perimeter of the shape = 3 × 0.75 π
∴ The perimeter of the shape = 7.0685835 cm
∴ The perimeter of the shape is 7.0685835 cm
